Generating the Cantor’s Set with Computer

The Cantor’s set is somewhat fascinating fractal, when one gets to more familiar with it.

The basic idea is to handle real number interval [0,1]. This is divided to three parts of same width removing the middle part. The remaining parts are again divided to three parts of same width removing always the middle part. This is continued infinitely.

The Cantor’s set consists of the points that are left in this process.

In the language of the set theory the Cantor’s set can be expressed as follows:

The union tells what doesn’t belong to the set.

I have used this formula to implement the Cantor’s set in my program. The idea is to examine the union interval and draw a pixel, when the point does belong to the set.